The theorem of existence of the ruptures in the probability scale was proved in 2010. The theorem is used to analyze and to partially answer to the basic questions of insurance. The question is “To insure or not”. The goal of this paper is to reveal pure mathematical aspects of insurance...

The proof of the theorem of existence of the ruptures, namely the proof of maximality, is improved. The theorem may be used in economics and explain the well-known problems such as Allais’ paradox. Illustrated examples of ruptures are presented.

In the classical Arrow-Borch-Raviv problem of demand for insurance contracts, it is well-known that the optimal insurance contract for an insurance buyer – or decision maker (DM) – is a deductible contract, when the insurer is a risk-neutral Expected-Utility (EU) maximizer, and when the DM...

We consider the indifference valuation of an uncertain monetary payoff from the perspective of an uncertainty averse decision maker. We study how the indifference valuation depends on the decision maker’s attitudes toward uncertainty. We obtain a characterization of comparative uncertainty...

Probability distributions with identical shape factor asymptotic limit formulas are defined as asymptotic equivalent distributions. The GB1, GB2, and Generalized Gamma distributions are examples of asymptotic equivalent distributions, which have similar fitting capabilities to data distribution...

The shape factor defined as kurtosis divided by skewness squared K/S^2 is characterized as the only choice among all factors K/〖|S|〗^α ,α0 which is greater than or equal to 1 for all probability distributions. For a specific distribution family, there may exists α2 such that...

A theorem of existence of the non-zero restrictions for the mean of a function on a finite numerical segment at a non-zero dispersion of the function is proved. The theorem has an applied character. It is aimed to be used in the probability theory and statistics and further in economics. Its...

In this paper I consider a portfolio optimization problem where an agent holds an endowment of stock and is allowed to buy some quantity of a put option on the stock. This basic question (how much insurance to buy?) has been addressed in insurance economics through the literature on rational...

I analyze a portfolio optimization problem where an agent holds an endowment of stock and is allowed to buy some quantity of a put option on the stock. My model rephrases a fundamental question from insurance economics: how much coverage should a risk averse agent buy? Classic studies of...

We consider economic obstacles that limit the reliability and accuracy of value-at-risk (VaR). Investors who manage large market transactions should take into account the impact of the randomness of large trade volumes on predictions of price probability and VaR assessments. We introduce...